Free Bayes Theorem Calculator
Apply Bayes' theorem to compute posterior probability from prior probability, likelihood, and evidence.
P(A|B) - Posterior
0.153846
P(A|B) - Posterior vs P(A) - Prior
How to Apply Bayes' Theorem
Formula
P(A where P(B) = P(B Bayes' theorem updates a prior belief P(A) after observing evidence B. The likelihood P(BB) = P(B A) * P(A) / P(B) A)*P(A) + P(B not A)*P(not A)
Example Calculation
A disease affects 1% of the population. A test is 90% sensitive and has a 5% false positive rate. If someone tests positive, what is the probability they have the disease?
- 01P(A) = 0.01 (prior: disease prevalence)
- 02P(B|A) = 0.9 (sensitivity)
- 03P(B|not A) = 0.05 (false positive rate)
- 04P(B) = 0.9 * 0.01 + 0.05 * 0.99 = 0.009 + 0.0495 = 0.0585
- 05P(A|B) = (0.9 * 0.01) / 0.0585 = 0.009 / 0.0585 ≈ 0.1538
- 06Despite a positive test, there is only about a 15.4% chance of having the disease.
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